Find each measurement indicated. Round your answers to the nearest tenth.
Find BC

Question

Find each measurement indicated. Round your answers to the nearest tenth.  Find BC

Kara Dillon · Accepted Answer

Step 1

Since, we are given the length of the sides AC and AB withmeasurement of 10 cm and 13 cm of a non right angled triangles with $137^{\circ}$ between them
Our aim is to find the length of the side BC of a triangle i.e, to find the value of $x = ?$
Step 2
Using Cosine Rule in finding the unlown lenth of the side which states that:
For any non−right angled triangle with sides a, b and c:−
$b^{2} = c^{2} + a^{2} - 2 c a \cos B$
$\Rightarrow x^{2} = {(10)}^{2} + {(13)}^{2} - 2 \times 10 \times 13 \times \cos (137^{\circ})$
$\Rightarrow x^{2} = 100 + 169 - (260 \times 0.334)$
$\Rightarrow x^{2} = 269 - 86.88$
$\Rightarrow x^{2} = 182.12$
$\Rightarrow x = \sqrt{182.12}$
$\Rightarrow x = 13.49 c m$
On rounding off to the nearest tenth we have $x = 13.5 c m$
Therefore, the length of the side BC is 13.5 cm.

Find each measurement indicated. Round your answers to the nearest tenth. Fi

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